Fractional Derivatives Applied to Phase-Space Reconstructions

The concept and application of phase-space reconstructions are reviewed. Fractional derivatives are then proposed for the purpose of reconstructing dynamics from a single observed time history. A procedure is presented in which the fractional derivatives of time series data are obtained in the frequency domain. The method is applied to the Lorenz system. The ability of the method to unfold the data is assessed by the method of global false nearest neighbors. The reconstructed data is used to compute recurrences and correlation dimensions. The reconstruction is compared to the commonly used method of delays in order to assess the choice of reconstruction parameters, and also the quality of results.     

Robust Speed Control of a Low Damped Electromechanical System Based on CRONE Control: Application to a Four Mass Experimental Test Bench

Robust speed control of a low damped electromechanical system with backlash is studied, controlled load angular speed being not measured. The proposed control strategy combines a Luenberger observer (load angular speed and load torque disturbance estimations) and a robust CRONE controller. The observer provides estimation of the load angular speed and of the disturbance torque applied on the load. Through the computation of only three independent parameters (as many as a PID controller), the CRONE controller permits to ensure the robust speed control of the load in spite of plant parametric variations and speed observation errors. The proposed control strategy is applied to a four mass experimental test bench.     

Order conditions for linearly implicit fractional step Runge Kutta methods

^{In this paper, we study the consistency of a variant of fractionalstep Runge–Kutta methods. These methods are designed tointegrate efficiently semi-linear multidimensional parabolicproblems by means of linearly implicit time integration processes.Such time discretization procedures are also related to a splittingof the space differential operator (or the spatial discretizationof it) as a sum of ‘simpler’ linear differentialoperators and a nonlinear term.}     

Motion Control by ZV Shaper Synthesis Extended for Fractional Systems and Its Application to CRONE Control

Shaping command input or preshaping is used for reducing system oscillation in motion control. Desired systems inputs are altered so that the system finishes the requested move without residual oscillation. This technique, developed by N.C. Singer and W.P. Seering, is used for example in the aerospace field, in particular in flexible structure control. This paper presents the study of ZV shaper for explicit fractional derivative systems (generalized derivative systems). A robustness study of ZV shaper is then presented and applied to improve second generation CRONE control response time. Results from simulation and from a DC motor bench are also given.     

Molecular dynamics simulations of pure methane and carbon dioxide hydrates: lattice constants and derivative properties

ABSTRACT

We report extensive molecular dynamics simulation results of pure methane and carbon dioxide hydrates at pressure and temperature conditions that are of interest to various practical applications. We focus on the calculation of the lattice constants of the two pure hydrates and their dependence on pressure and temperature. The calculated lattice constants are correlated using second order polynomials which are functions of either temperature or pressure. Finally, the obtained correlations are used in order to calculate two derivative properties, namely the isothermal compressibility and the isobaric thermal expansion coefficient. The current simulation results are also compared against reported experimental measurements and other simulation studies and good agreement is found for the case of isothermal compressibility. On the other hand, for the case of isobaric thermal expansion coefficient good agreement is found only with other simulation studies, while the simulation studies are in disagreement with experiments, particularly at low temperatures.     

傅里叶红外光谱法鉴别部分胡椒属生药的研究

利用共有峰率和变异峰率双指标,以胡椒属七种药用植物的红外指纹图谱为依据,计算出所测样品的共有峰率和变异峰率。建立了胡椒属七种药用植物共有峰率和变异峰率双指标序列,结果揭示了胡椒属七种药用植物的亲缘关系。中药海风藤与石南藤、大叶蒟根茎的共有峰率均在77%以上,变异峰率均在30%以下,此三种胡椒属药用植物亲缘关系较近;海风藤与胡椒根茎、十八症根的共有峰率在61%左右,亲缘关系稍远;海风藤与蒌叶根茎的共有峰率仅为44%。亲缘关系较远。利用红外二阶导数谱图,可以鉴别中药海风藤及其伪品石南藤、十八症根、大叶蒟根茎、胡椒根茎等品种。傅里叶红外光谱法可以对样品进行无损处理,不需要对药材进行复杂的提取分离过程即可提供化合物的官能团、类别、氢键等信息。该法能从整体水平分析谱图特征峰,具有分析速度快,重现性好,非破坏性和样品量小,制样简单,专属性强,节约成本,保护环境等优点。可以解决中药海风藤因资源短缺,伪品较多,鉴别困难等问题,也可为临床用药的安全、有效提供保障。傅里叶红外光谱法为胡椒属药用植物亲缘关系的探讨和真伪鉴别提供了一种新方法。符合中药向综合分析和整体分析发展的趋势。     

Stochastic model for market stocks with floors

We present a model to describe the stochastic evolution of stocks that show a strong resistance at some level and generalize to this situation the evolution based upon geometric Brownian motion. If volatility and drift are related in a certain way we show that our model can be integrated in an exact way. The related problem of how to prize general securities that pay dividends at a continuous rate and earn a terminal payoff at maturity T is solved via the martingale probability approach.     

Alternating direction implicit schemes for the two-dimensional fractional sub-diffusion equation

New numerical techniques are presented for the solution of a two-dimensional anomalous sub-diffusion equation with time fractional derivative. In these methods, standard central difference approximation is used for the spatial discretization, and, for the time stepping, two new alternating direction implicit (ADI) schemes based on the L₁ approximation and backward Euler method are considered. The two ADI schemes are constructed by adding two different small terms, which are different from standard ADI methods. The solvability, unconditional stability and H¹ norm convergence are proved. Numerical results are presented to support our theoretical analysis and indicate the efficiency of both methods.     

Characteristics of high energy interactions II. Production spectra of Gamma-rays in graphite

Twenty high energy nuclear interactions produced in the graphite units of an emulsion chamber were recorded. The emulsion chamber was exposed to cosmic rays at an atmospheric depth of 10 g cm⁻² for about 7 hr over Hyderabad, India. Fourteen interactions which radiated energyΣ E _r⩾1000 GeV in the form ofγ-rays were analysed in detail. The median energy 〈Σ E _r〉 of the interactions was 1600 GeV. Results concerning the multiplicity, the transverse and longitudinal momentum distributions, and the fractional energy distribution ofγ-rays in these interactions are presented. The average transverse momentum ofπ ⁰—mesons <pt _π ⁰> is found to increase very slowly with the primary energyE ₀ and it can be approximated by the function <pt _π ⁰>=0·238E ₀ ^0.06 .     

Equivalent quasi-norms on Lorentz spaces

We give new characterizations of Lorentz spaces by means of certain quasi-norms which are shown to be equivalent to the classical ones.